Numerical algebraic geometry for model selection and its application to the life sciences

Researchers working with mathematical models are often confronted by the related problems of parameter estimation, model validation, and model selection. These are all optimization problems, well-known to be challenging due to non-linearity, non-convexity and multiple local optima. Furthermore, the challenges are compounded when only partial data is available. Here, we consider polynomial models (e.g., mass-action chemical reaction networks at steady state) and describe a framework for their analysis based on optimization using numerical algebraic geometry. Specifically, we use probability-one polynomial homotopy continuation methods to compute all critical points of the objective function, then filter to recover the global optima. Our approach exploits the geometric structures relating models and data, and we demonstrate its utility on examples from cell signaling, synthetic biology, and epidemiology.Comment: References added, additional clarification

U. S. labor supply and demand in the long run

In this paper we model U.S. labor supply and demand in considerable detail in order to capture the enormous heterogeneity of the labor force and its evolution over the next 25 years. We represent labor supplies for a large number of demographic groups as responses to prices of leisure and consumption goods and services. The price of leisure is an after-tax wage rate, while the final prices of goods and services reflect the supply prices of the industries that produce them. By including demographic characteristics among the determinants of household preferences, we incorporate the expected demographic transition into our long-run projections of the U.S. labor market.Labor supply ; Labor market

Cooling of the Cassiopeia A neutron star and the effect of diffusive nuclear burning

The study of how neutron stars cool over time can provide invaluable insights into fundamental physics such as the nuclear equation of state and superconductivity and superfluidity. A critical relation in neutron star cooling is the one between observed surface temperature and interior temperature. This relation is determined by the composition of the neutron star envelope and can be influenced by the process of diffusive nuclear burning (DNB). We calculate models of envelopes that include DNB and find that DNB can lead to a rapidly changing envelope composition which can be relevant for understanding the long-term cooling behavior of neutron stars. We also report on analysis of the latest temperature measurements of the young neutron star in the Cassiopeia A supernova remnant. The 13 Chandra observations over 18 years show that the neutron star's temperature is decreasing at a rate of 2-3 percent per decade, and this rapid cooling can be explained by the presence of a proton superconductor and neutron superfluid in the core of the star.Comment: 7 pages, 7 figures; to appear in the AIP Conference Proceedings of the Xiamen-CUSTIPEN Workshop on the EOS of Dense Neutron-Rich Matter in the Era of Gravitational Wave Astronomy (January 3-7, 2019, Xiamen, China

The Structure of Nuclear Star Clusters in Nearby Late-type Spiral Galaxies from Hubble Space Telescope Wide Field Camera 3 Imaging

We obtained Hubble Space Telescope/Wide Field Camera 3 imaging of a sample of ten of the nearest and brightest nuclear clusters residing in late-type spiral galaxies, in seven bands that span the near-ultraviolet to the near-infrared. Structural properties of the clusters were measured by fitting two-dimensional surface brightness profiles to the images using GALFIT. The clusters exhibit a wide range of structural properties. For six of the ten clusters in our sample, we find changes in the effective radius with wavelength, suggesting radially varying stellar populations. In four of the objects, the effective radius increases with wavelength, indicating the presence of a younger population which is more concentrated than the bulk of the stars in the cluster. However, we find a general decrease in effective radius with wavelength in two of the objects in our sample, which may indicate extended, circumnuclear star formation. We also find a general trend of increasing roundness of the clusters at longer wavelengths, as well as a correlation between the axis ratios of the NCs and their host galaxies. These observations indicate that blue disks aligned with the host galaxy plane are a common feature of nuclear clusters in late-type galaxies, but are difficult to detect in galaxies that are close to face-on. In color-color diagrams spanning the near-UV through the near-IR, most of the clusters lie far from single-burst evolutionary tracks, showing evidence for multi-age populations. Most of the clusters have integrated colors consistent with a mix of an old population (> 1 Gyr) and a young population (~100-300 Myr). The wide wavelength coverage of our data provides a sensitivity to populations with a mix of ages that would not be possible to achieve with imaging in optical bands only.Comment: Corrected a typo in author name and affiliation for MC and corrected a typo in the conclusio